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Physical growth traits can be naturally represented by continuous functions. In a large dataset of infancy growth patterns, we develop a practical approach to infer statistical associations between growth-trajectories and IQ performance in early childhood. The main objective of this study is to show how to assess physical growth curves and detect if particular infancy growth patterns are associated with differences in IQ (Full-scale WASI scores) in later ages using a semi-parametric functional response model. Additionally, we investigate the association between different growth measurements in terms of their cross-correlation with each other, their correlation with later IQ, as well as their time-varying dynamics. This analysis framework can easily incorporate or learn population information in a non-parametric way, rendering the existence of prior population charts partially redundant.

The historical and geographical spread from older to more modern languages has long been studied by examining textual changes and in terms of changes in phonetic transcriptions. However, it is more difficult to analyze language change from an acoustic point of view, although this is usually the dominant mode of transmission. We propose a novel analysis approach for acoustic phonetic data, where the aim will be to statistically model the acoustic properties of spoken words. We explore phonetic variation and change using a time-frequency representation, namely the log-spectrograms of speech recordings. We identify time and frequency covariance functions as a feature of the language; in contrast, mean spectrograms depend mostly on the particular word that has been uttered. We build models for the mean and covariances (taking into account the restrictions placed on the statistical analysis of such objects) and use these to define a phonetic transformation that models how an individual speaker would sound in a different language, allowing the exploration of phonetic differences between languages. Finally, we map back these transformations to the domain of sound recordings, allowing us to listen to the output of the statistical analysis. The proposed approach is demonstrated using recordings of the words corresponding to the numbers from "one" to "ten" as pronounced by speakers from five different Romance languages.

Mandarin Chinese is characterized by being a tonal language; the pitch (or $F_0$) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in amplitude and phase which must be accounted for in any analysis which attempts to provide a linguistically meaningful description of the language. A joint model for amplitude, phase and duration is presented which combines elements from Functional Data Analysis, Compositional Data Analysis and Linear Mixed Effects Models. By decomposing functions via a functional principal component analysis, and connecting registration functions to compositional data analysis, a joint multivariate mixed effect model can be formulated which gives insights into the relationship between the different modes of variation as well as their dependence on linguistic and non-linguistic covariates. The model is applied to the COSPRO-1 data set, a comprehensive database of spoken Taiwanese Mandarin, containing approximately 50 thousand phonetically diverse sample $F_0$ contours (syllables), and reveals that phonetic information is jointly carried by both amplitude and phase variation., Comment: 49 pages, 13 figures, small changes to discussion

Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical statistical approach to infer ancestral function-valued traits, and estimate the generative evolutionary process. We do this by combining dimension reduction and phylogenetic Gaussian process regression, a nonparametric procedure which explicitly accounts for known phylogenetic relationships. We test the methods' performance on simulated function-valued data generated from a stochastic evolutionary model. The methods are applied assuming that only the phylogeny and the function-valued traits of taxa at its tips are known. Our method is robust and applicable to a wide range of function-valued data, and also offers a phylogenetically aware method for estimating the autocorrelation of function-valued traits.

Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Here we use phylogenetic Gaussian process regression to model the evolution of simulated function-valued traits. Given function-valued data only from the tips of an evolutionary tree and utilising independent principal component analysis (IPCA) as a method for dimension reduction, we construct distributional estimates of ancestral function-valued traits, and estimate parameters describing their evolutionary dynamics.